Asymptotic Behavior of a Class of Nonlinear Stochastic Heat Equations with Memory Effects

DOI10.1137/110841795zbMath1247.60099OpenAlexW1989508702MaRDI QIDQ2902731

Luciano Tubaro, Stefano Bonaccorsi, Giuseppe Da Prato

Publication date: 22 August 2012

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/110841795

zbMATH Keywords

asymptotic behaviourstationary solutionuniqueness of invariant measureintegral stochastic equation

Mathematics Subject Classification ID

Markov semigroups and applications to diffusion processes (47D07) Volterra integral equations (45D05) Stochastic integral equations (60H20)

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Large deviations for stochastic heat equations with memory driven by Lévy-type noise ⋮ Optimal control for stochastic Volterra equations with multiplicative Lévy noise ⋮ On the Hölder regularity of a linear stochastic partial-integro-differential equation with memory ⋮ Some approximation results for mild solutions of stochastic fractional order evolution equations driven by Gaussian noise ⋮ The small mass limit for long time statistics of a stochastic nonlinear damped wave equation ⋮ Polynomial mixing of a stochastic wave equation with dissipative damping ⋮ Optimal control for stochastic heat equation with memory ⋮ Existence and uniqueness of solutions to stochastic functional differential equations in infinite dimensions ⋮ Existence, uniqueness and regularity for a class of semilinear stochastic Volterra equations with multiplicative noise ⋮ Existence and asymptotic behavior for hereditary stochastic evolution equations ⋮ Global solutions to stochastic Volterra equations driven by Lévy noise ⋮ Ergodicity of a nonlinear stochastic reaction-diffusion equation with memory

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